Please can you help me with this practice question from my lecture. I have completed the question already and just need some compare it. Thank you for any help!

Suppose Robinson Crusoe produces Coconut (C) and Fish (F) using only labour and the production functions are: = 10 and = and represent labour devoted to the production of coconut and fish, respectively, and >0 is a constant. Suppose labour supply is fixed at L = 400, and the utility function of Crusoe is = .

How do the equilibrium quantities and price ratio change when increases? Explain the intuition behind your mathematical results.

Please give a good answer with detail and solid mathematical results and I will leave a fantastic review!